2. Alex sets two alarm clocks each night to ensure that he does not sleep through his 9:00 a.m. class. His primary clock properly sounds its alarm on 80% of the mornings, while his secondary clock rings its bell on only 70% of mornings. Assume the clocks operate independently. a) (3) What percent of the time does Alex’s two-clock strategy prevent him from oversleeping? That is, find the probability that at least one alarm would sound on a given morning. P( 1st OR 2nd ) = P( 1st ) + P( 2nd ) – P( 1st AND 2nd ) = 0.80 + 0.70 – 0.80 × 0.70 = 0.94 . OR P( at least one ) = 1 – P( none ) = 1 – 0.20 × 0.30 = 0.94 . b) (3) Find the probability that only one alarm would sound on a given morning. P( 1st only ) + P( 2nd only ) = 0.80 × 0.30 + 0.20 × 0.70 = 0.38 . 3. (3) Suppose an individual is randomly selected from the population of adult males living in the United States. Let A be the event that the selected individual is over 6 ft. in height, and let B be the event that the selected individual is a professional basketball player. Which do you think is larger, P( A | B ) or P( B | A ), and why ? ( Circle one and

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